SRB measures for partially hyperbolic systems whose central direction is weakly expanding

• Type: Article in International Scientific Journal
• Date: 2017

Authors

alves, jf (Author) FCUP; Dias, CL (Author) Other; Luzzatto, S (Author) Other; Pinheiro, V (Author) Other

Journal

Title: Journal of the European Mathematical Society

Vol. 19

Pages: 2911-2946

ISSN: 1435-9855

Publisher: European Mathematical Society Publishing House

Indexing

ISI Web of Knowledge - 14 Citations

Scopus - 19 Citations

Other information

Authenticus ID: P-00N-53W

DOI: 10.4171/jems/731

Abstract (EN): We consider partially hyperbolic C1+ diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition E-s circle plus E-cu. Assuming the existence of a set of positive Lebesgue measure on which f satisfies a weak nonuniform expansivity assumption in the centre unstable direction, we prove that there exist at most a finite number of transitive attractors each of which supports an SRB measure. As part of our argument, we prove that each attractor admits a Gibbs-Markov-Young geometric structure with integrable return times. We also characterize in this setting SRB measures which are liftable to Gibbs-Markov-Young structures.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 36